Stress tensor fluctuations in de Sitter spacetime

The two-point function of the stress tensor operator of a quantum field in de Sitter spacetime is calculated for an arbitrary number of dimensions. We assume the field to be in the Bunch-Davies vacuum, and formulate our calculation in terms of de Sitter-invariant bitensors. Explicit results for free minimally coupled scalar fields with arbitrary mass are provided. We find long-range stress tensor correlations for sufficiently light fields (with mass m much smaller than the Hubble scale H), namely, the two-point function decays at large separations like an inverse power of the physical distance with an exponent proportional to m^2/H^2. In contrast, we show that for the massless case it decays at large separations like the fourth power of the physical distance. There is thus a discontinuity in the massless limit. As a byproduct of our work, we present a novel and simple geometric interpretation of de Sitter-invariant bitensors for pairs of points which cannot be connected by geodesics.Comment: 35 pages, 4 figure

Moving constraints as stabilizing controls in classical mechanics

The paper analyzes a Lagrangian system which is controlled by directly assigning some of the coordinates as functions of time, by means of frictionless constraints. In a natural system of coordinates, the equations of motions contain terms which are linear or quadratic w.r.t.time derivatives of the control functions. After reviewing the basic equations, we explain the significance of the quadratic terms, related to geodesics orthogonal to a given foliation. We then study the problem of stabilization of the system to a given point, by means of oscillating controls. This problem is first reduced to the weak stability for a related convex-valued differential inclusion, then studied by Lyapunov functions methods. In the last sections, we illustrate the results by means of various mechanical examples.Comment: 52 pages, 4 figure

Hilbert Expansion from the Boltzmann equation to relativistic Fluids

We study the local-in-time hydrodynamic limit of the relativistic Boltzmann equation using a Hilbert expansion. More specifically, we prove the existence of local solutions to the relativistic Boltzmann equation that are nearby the local relativistic Maxwellian constructed from a class of solutions to the relativistic Euler equations that includes a large subclass of near-constant, non-vacuum fluid states. In particular, for small Knudsen number, these solutions to the relativistic Boltzmann equation have dynamics that are effectively captured by corresponding solutions to the relativistic Euler equations.Comment: 50 page

Conformal Transformations in Cosmology of Modified Gravity: the Covariant Approach Perspective

The 1+3 covariant approach and the covariant gauge-invariant approach to perturbations are used to analyze in depth conformal transformations in cosmology. Such techniques allow us to obtain very interesting insights on the physical content of these transformations, when applied to non-standard gravity. The results obtained lead to a number of general conclusions on the change of some key quantities describing any two conformally related cosmological models. In particular, it is shown that the physics in the Einstein frame has characteristics which are completely different from those in the Jordan frame. Even if some of the geometrical properties of the cosmology are preserved (homogeneous and isotropic Universes are mapped into homogeneous and isotropic universes), it can happen that decelerating cosmologies are mapped into accelerated ones. Differences become even more pronounced when first-order perturbations are considered: from the 1+3 equations it is seen that first-order vector and tensor perturbations are left unchanged in their structure by the conformal transformation, but this cannot be said of the scalar perturbations, which include the matter density fluctuations. Behavior in the two frames of the growth rate, as well as other evolutionary features, like the presence or absence of oscillations, etc., appear to be different too. The results obtained are then explicitly interpreted and verified with the help of some clarifying examples based on $f(R)$-gravity cosmologies.Comment: 26 pages, 8 figure

Energy and Momentum Densities Associated with Solutions Exhibiting Directional Type Singularities

We obtain the energy and momentum densities of a general static axially symmetric vacuum space-time described by the Weyl metric, using Landau-Lifshitz and Bergmann-Thomson energy-momentum complexes. These two definitions of the energy-momentum complex do not provide the same energy density for the space-time under consideration, while give the same momentum density. We show that, in the case of Curzon metric which is a particular case of the Weyl metric, these two definitions give the same energy only when $R \to \infty$. Furthermore, we compare these results with those obtained using Einstein, Papapetrou and M{\o}ller energy momentum complexes.Comment: 10 pages, references added, minor corrections [Admin note: substantial overlap with gr-qc/0403097 , gr-qc/0403039

The Irish Rover: Phil Lynott and the Search for Identity

Phil Lynott, the lead singer of the rock band Thin Lizzy, was a complex character. An illegitimate black child who grew up in a working-class, Catholic district of Dublin, Ireland in the 1950s, Lynott spent his life searching for a sense of belonging, something which he explored through rock and roll. This study uses Lynott’s song lyrics to investigate his quest for identity. In particular, it identifies the many recurring themes and archetypes in his music that offered multifaceted self-portraits of his internal conflict between being black, Irish, illegitimate, a rockstar, a Lothario, a son, a father, and a husband, all at the same time

Luasnad, Capa y Laine

Traducción de Francisco Javier Torres Ribelle

The Playboy of the western world and riders to the sea

93 p.; 18 cm

Fragmento de una obra inacabada: obra vernal

Fragments of an unfinished play: a vernal play = Fragmento de una obra inacabada: obra vernal / translated by Brian Hughes and Francisco Javier Torres Ribelle